Tangent–secant Theorem
In Euclidean geometry, the tangent-secant theorem describes the relation of line segments created by a Secant line, secant and a tangent line with the associated circle. This result is found as Proposition 36 in Book 3 of Euclid's Euclid's Elements, ''Elements''. Given a secant intersecting the circle at points and and a tangent intersecting the circle at point and given that and intersect at point , the following equation holds: , PT, ^2=, PG_1, \cdot, PG_2, The tangent-secant theorem can be proven using similar triangles (see graphic). Like the intersecting chords theorem and the intersecting secants theorem, the tangent-secant theorem represents one of the three basic cases of a more general theorem about two intersecting lines and a circle, namely, the Power of a point, power of point theorem. References *S. Gottwald: ''The VNR Concise Encyclopedia of Mathematics''. Springer, 2012, , pp175-176*Michael L. O'Leary: ''Revolutions in Geometry''. Wiley, 2010, , p161 ...
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